This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equations that support arbitrary orders and polyhedral meshes. Unlike other methods presented in the literature, pressure-robustness is achieved here without resorting to an H(div)-conforming construction on a submesh, but rather projecting the volumetric force onto the discrete H(curl) space. The cancellation of the pressure error contribution stems from key commutation properties of the underlying DDR and VEM complexes. The pressure-robust error estimates in hk+1 (with h denoting the meshsize and k≥0 the polynomial degree of the DDR or VEM complex) are proven theoretically and supported by a panel of three-dimensional numerical tests. The second major contribution of the paper is an in-depth study of the relations between the DDR and VEM approaches. We show, in particular, that a complex developed following one paradigm admits a reformulation in the other, and that couples of related DDR and VEM complexes satisfy commuting diagram properties with the degrees of freedom maps.

Beirao da Veiga, L., Dassi, F., Di Pietro, D., Droniou, J. (2022). Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 397(1 July 2022) [10.1016/j.cma.2022.115061].

Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes

Beirao da Veiga, L
;
Dassi, F
;
2022

Abstract

This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equations that support arbitrary orders and polyhedral meshes. Unlike other methods presented in the literature, pressure-robustness is achieved here without resorting to an H(div)-conforming construction on a submesh, but rather projecting the volumetric force onto the discrete H(curl) space. The cancellation of the pressure error contribution stems from key commutation properties of the underlying DDR and VEM complexes. The pressure-robust error estimates in hk+1 (with h denoting the meshsize and k≥0 the polynomial degree of the DDR or VEM complex) are proven theoretically and supported by a panel of three-dimensional numerical tests. The second major contribution of the paper is an in-depth study of the relations between the DDR and VEM approaches. We show, in particular, that a complex developed following one paradigm admits a reformulation in the other, and that couples of related DDR and VEM complexes satisfy commuting diagram properties with the degrees of freedom maps.
Articolo in rivista - Articolo scientifico
Compatible discretizations; Discrete de Rham method; Polyhedral methods; Pressure-robustness; Stokes problem; Virtual element method
English
7-giu-2022
2022
397
1 July 2022
115061
none
Beirao da Veiga, L., Dassi, F., Di Pietro, D., Droniou, J. (2022). Arbitrary-order pressure-robust DDR and VEM methods for the Stokes problem on polyhedral meshes. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 397(1 July 2022) [10.1016/j.cma.2022.115061].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/394879
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